Abstract
On the basis of qualitative considerations of quantum fluctuations in the space-time geometry, a modification of the Feynman propagator is proposed involving a smearing of the propagator over a space-time region of an extent of about a Planck length, or $\ensuremath{\simeq}{10}^{\ensuremath{-}33}\mathrm{cm},$ surrounding the light cone. The smeared propagator is a weighted average of modified Bessel functions both in coordinate space and in momentum space. In coordinate space, the smeared propagator has a milder singularity on the light cone than the Feynman propagator, and in momentum space it provides an effective cutoff at the Planck mass. Radiative corrections in QED can be easily calculated with this propagator, and the results are finite. The renormalizations of the electron charge and mass are of the order of a few percent.
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